Step 1 :Given: \(\angle 1\) and \(\angle 3\) are vertical angles
Step 2 :Prove: \(\angle 1 \cong \angle 3\)
Step 3 :Statements: \(\angle 1\) and \(\angle 2\) are supplementary, \(\angle 2\) and \(\angle 3\) are supplementary
Step 4 :Reasons: Linear pair postulate, Linear pair postulate
Step 5 :\(\angle 1 \cong \angle 3\) because if two angles are supplementary to the same angle, then they are congruent (Transitive Property of Equality)
Step 6 :Final Answer: \(\boxed{\angle 1 \cong \angle 3}\), which is the Vertical Angles Theorem